Either word works. It’s hyper-specific but I would say that most people would say “rung” in reference to the physical part of the ladder while “step” would be the part of the ladder they were on.

Again, either word works fine and nobody would bat an eye if either were used.

Good question!

Technically there is a type of ‘step ladder’ thet has wider flat ‘steps’ more like a staircase. Rungs are the narrower round bars on a more traditional ‘ladder’.

But practically either word can be used in either case. You can either ‘step’ or ‘climb’ as the verb in either case too.